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ISE529 categorical variable
Creation date：2024-06-11 17:37:46
Belonging category：数学mathematics
Tag ISE529
categorical variable

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ISE529 HW3

Note: Submit the .Rmd file and the output PDF file in blackboard before the deadline. We will grade your
last submitted work before the deadline.
Question 1
In this exercise, you will explore logistic regression. You will work with a synthetic dataset that simulates
customer data for a subscription service.
The goal is to predict whether a customer will subscribe (1) or not subscribe (0) to a service based on their
age and whether they are a student. The “student” variable is categorical (Yes/No) and will be used as an
indicator variable in your logistic regression model.
Tasks:
Note: For reproducibility, set the seed deliberately in your code for task 1. You can choose any number you
like but try one that is unique to you, such as the last four digits of your student ID.
1. Data Generation:
Create a synthetic dataset with 200 observations that include the following variables:
• age: A integer variable representing the customer’s age, randomly generated from a uniform distribution,
between 18 and 80.
• student: A categorical variable (label: Yes/No) indicating whether the customer is a student, randomly
assigned.
• subscribe: A binary outcome variable (1/0) indicating whether the customer subscribes to the service.
You will generate this variable based on a logistic function that includes the effects of age and student
status, with some added random noise to simulate a realistic scenario.
The logistic function is of the form 11+e−z as discussed in class, where z is a linear combination of
predictor variables and β0 = −9, βage = 0.02, βstudent = 3.5. Next, you need to generate the binary
outcome for the logistic regression. Hint: rbinom() may be useful.
2. Logistic Regression Model:
Fit a logistic regression model to predict the probability of subscription (subscribe) using age and
student as predictors. Note: make sure you handle student as an indicator variable.
3. Model Interpretation:
Interpret the coefficients of your model: discuss how age, and student status influence the subscription
likelihood.
4. Model Evaluation:
Evaluate your model using at least two metrics: accuracy, confusion matrix, ROC curve, etc. Interpret
your model performance based on these metrics.
5. Discussion:
Discuss the implications of using indicator variables in logistic regression models. How do they affect
the interpretation of model coefficients?
Question 2
In this exercise, you will explore the K-Nearest Neighbors (KNN) algorithm, a fundamental technique in
statistical Machine Learning for classification problems. You will generate synthetic data to simulate a 2-class
1
classification problem, apply KNN using different values of K, and analyze how the choice of K affects the
model’s decision boundary, misclassification rate, and the concepts of bias and variance. Finally, you will split
your data into training and test sets to identify an optimal K and discuss the implications of this method for
model selection.
Tasks:
Note: For reproducibility, set the seed as in the previous question.
1. Data Generation:
• Generate 100 random data points to simulate a 2-class classification problem, with 50 points for each
class. Use a normal distribution N(0,1) for the first class and N(2,1) for the second class.
• Note: each random data point generated should be (x,y) indicating the position of a point in the 2D
coordinate plane. Both classes share the same standard deviation but differ in their means.
2. KNN Fitting and Misclassification Rate Calculation:
• Fit the KNN classifier to your data using several different values of K = (3, 5, 7, 9).
• For each K, calculate the misclassification rate by comparing the predicted class labels against the true
labels.
3. Decision Boundary Plotting:
• Using base R plotting functions, plot the decision boundary for each K. Use different colors to represent
the different classes.
• Evaluate how the decision boundary changes with different values of K.
4. Variance and Bias Discussion:
• Discuss the concepts of variance and bias in the context of KNN. How do these concepts relate to the
choice of K?
5. Model Selection with Test/Train Split:
• Randomly split your data into a training set (70%) and a test set (30%).
• Refit the KNN model using the training data and evaluate the performance on the test data to choose
an optimal K. Carefully explain your steps.
• Discuss any potential issues with this method of selecting K.
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CMP7000A CMP-7038B Math 263 LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 ​COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 ​BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 ​LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ​ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 ​FINC5090 ​MATH1052 ​SciComp Elec4622 ​FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 ​MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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